Role of Artificial Intelligence in Film and Entertainment:A Topological Matrix and Differential Modelling Framework

Abstract: Artificial intelligence is becoming a structural force in film and entertainment by influencing script development, editing, visual effects, audience analytics, recommendation systems, marketing, and platform distribution. This research paper develops a formal AI-FE Topological Matrix Framework to evaluate the measurable role of AI in film and entertainment outcomes. The framework combines linear algebra, topological metric spaces, and differential modelling to represent the relationship between AI adoption and industry performance. The study proposes five AI input variables: AI-supported script development, AI editing, AI-generated visual effects, AI-based recommendation systems, and AI-enabled marketing. These inputs are mapped into five outcome dimensions: creativity, production efficiency, VFX quality, audience engagement, and distribution performance. A numerical demonstration using normalized 0-10 scores produces a matrix-based AI score of 6.56, a topological structure score of 6.60, and a final integrated outcome score of 6.08 after risk adjustment. The model shows that AI contributes most strongly to VFX and production outcomes, while copyright, labour, ethical, cultural, and originality risks reduce the final measurable benefit. The paper does not claim empirical proof from primary industry data; rather, it provides a reproducible framework that can be validated through surveys, platform analytics, production datasets, and audience-behaviour records. The proposed framework is useful for researchers, studios, OTT platforms, policymakers, and creative-industry managers seeking a structured method to measure AI impact while integrating responsible AI governance. Keywords: Artificial intelligence; film analytics; entertainment technology; generative AI; visual effects; audience analytics; linear algebra; topological data analysis; differential modelling; creative industry governance